This project seeks to develop alternatives to the commonly used integration methods by which molecular dynamics trajectories are generated. Typically, these methods suffer from the fact that the largest time step that can be used in the integration, after which the forces must be recalculated, is of the order of only 1 or 2 fs. Given limited amounts of computing time, the total time that can be simulated for any given system is severely limited, and this again limits the extent to which equilibrium states can be sampled and kinetic processes can be followed. The alternative methods seek to use larger time steps; generally this requires some additional computational effort for auxiliary calculations, but the goal is a net decrease of the ratio of computer time to simulated time. The NYU group has developed a method based on normal modes and implicit integration, "LIN", and this method has passed the important break-even milestone last year. By solution of the linearized equations of motion numerically, rather than analytically, and by optimization of other components of the method (via adaptive time step selection and accelerated minimization), the additional work required to implement the implicit solver (which makes the large time step possible) was more than compensated for by the decreased number of steps required to cover the same simulation time. Tests of LIN on a model dipeptide and the small protein BPTI showed excellent agreement of LIN with time steps of 15 fs (30 fs for the dipeptide) in comparison with explicit trajectories generated at time steps of 0.5 fs. A delightful surprise also emerged from these studies which addressed the computational competitiveness of LIN. Namely, examination of the range of validity of the harmonic approximation led also to development of a related method termed LN, which includes LIN's linearization, but not correction, step. LN at a time step of 5 fs also shows very good agreement with traditional MD and already for BPTI (904 atoms) gives a speedup factor of 4.35 on a serial machine. Moreover, speedup of LN will increase with size, and the method can be readily implemented in general biomolecular dynamics programs. This unexpected windfall illustrates the value of developing novel approaches (e.g., based on normal-mode techniques) that might initially appear not practical for macromolecules.